Which option is the solution to the inequality −12g+18>−5g+53 ? Responses g>−5 g greater than negative 5 g>71−17 g greater than Start Fraction 71 over negative 17 End Fraction g<−5 g less than negative 5 g<71−17
The solution to the inequality −12g+18>−5g+53 is given by the option g<71−17.
To find the solution to the inequality −12g+18 > −5g+53, we'll start by simplifying the equation:
−12g + 18 > −5g + 53
Next, let's combine like terms by adding 5g to both sides:
−12g + 5g + 18 > −5g + 5g + 53
Simplifying further:
−7g + 18 > 53
Next, let's subtract 18 from both sides to isolate the variable:
−7g + 18 - 18 > 53 - 18
Simplifying further:
−7g > 35
To solve for g, divide both sides of the inequality by -7 (note: since we are dividing by a negative number, the direction of the inequality sign will be reversed):
−7g / -7 < 35 / -7
Simplifying further gives:
g < -5
Therefore, the solution to the inequality −12g + 18 > −5g + 53 is g < -5.
To determine the solution to the inequality −12g + 18 > −5g + 53, we need to isolate the variable g.
We will first combine the like terms on both sides of the inequality:
−12g + 18 > −5g + 53
Next, we can simplify the equation:
−12g + 18 + 5g > −5g + 5g + 53
Simplifying further, we get:
−7g + 18 > 53
Now, we want to get rid of the constant term on the left side of the inequality. We can do this by subtracting 18 from both sides:
−7g + 18 - 18 > 53 - 18
This simplifies to:
−7g > 35
Next, we will divide both sides of the inequality by −7. It is important to remember that when we divide or multiply both sides of an inequality by a negative number, we need to reverse the inequality sign:
−7g / −7 < 35 / −7
Simplifying further, we get:
g < −5
Therefore, the solution to the inequality −12g + 18 > −5g + 53 is g < −5.